1. Field of the Invention
This invention relates to a damper, and more particularly to a splined tubular telescopic, double acting resilient unit for incorporation in a drill string, next to the bit or higher up in the string, of a rotary drilling system for earth boring, e.g., petroleum well drilling.
2. Description of the Prior Art
The prior art is discussed at length in the aforementioned Garrett application, including art relating to double acting dampers, variable spring rate dampers, sealed lubricated spring-spline-bearing means, floating seals, parallel spring means, double acting springs, elastomer-metal sandwich springs and Belleville springs.
A form of variable lever arm Belleville spring per se, of the general type employed in the present invention, is disclosed in U.S. Pat. No. 2,675,225--Migny. However Migny does not appear to disclose the concept of roller Belleville springs, only variable moment, i.e. variable lever arm, Belleville springs.
In one embodiment Migny shows only a single Belleville washer which is double convex in cross-section and is disposed between two flat plates. As load is imposed on the plates, the washer initially pivots about its upper inner edge and its lower outer edge as do ordinary Belleville springs, with a resultant linear force deflection curve, but as the washer flattens the washer's edges leave contact with the plates and force is transmitted to the washer through body areas inward of the edges, decreasing the lever arm and causing the force-deflection curve to become non-linear.
The initial pivoting of the Migny washer is of course not a rolling action but a pivot or hinge type action. Even when the washer turns so that its edges are out of contact with the plates, the washer does not roll on the plates but instead slides relative thereto, because the curvature of the washer faces is different from that of the plates, because the plates do not expand under load the same as the washers, and because the curvature of the bottom of each washer apparently differs from that of the top of each washer.
In another embodiment Migny discloses a stack of groups of Belleville spring washers. The groups are in series and the washers in each group are in parallel. The conical abutting surfaces of the paralleled washers in each group slide relative to each other as load is applied. Only the outer faces of the uppermost and lowermost washers in each group have convex sections. The latter washers may initially pivot relative to each other as does the washer of the first mentioned embodiment, and thereafter it is uncertain what the relative motion of the washers may be, for although such motion is described as being a "rocking" motion, the convex cross-section surfaces of the springs are said to be curved like the washers of the first described embodiment and the drawing appears to show different curvature on different washers.
At least it can be said that Migny does not discuss rolling or the conditions required to effect rolling of variable moment Belleville springs.
Early forms of drill string dampers are exemplified by patents such as German No. 631398 (1936)--Prussiche, U.S. Pat. No. 2,991,935--Warren, wherein a splined tubular telescopic joint is provided with a helical spring means urging the joint to extended position. These are single acting dampers, in that in the unstrained or neutral position of the damper, only contraction is possible, it being intended that in use the static load on the damper will compress the spring approximately half way, thereby to allow for resilient motion in both directions when the bit moves up and down.
For various reasons it has been disclosed that a variable modulus spring should be employed in a drill string damper. In this regard see U.S. Pat. Nos. 3,381,126--Salvatori; 3,409,537--Falkner; 3,871,193--Young; 3,949,150--Mason.
The foregoing patents showing variable modulus dampers relate to single acting dampers. It may be assumed that these dampers, like other single acting dampers, are intended to operate about a static deflection point near the mid-range of the load-deflection curve. In this regard, note the Mason patent wherein operation with a static load of 25,000 lb/in is described (col. 10, l. 63) with respect to a preferred variable spring rate curve as shown in the shaded area in FIG. 15 of the patent (col. 10, l. 6-10).
The dampers of the foregoing patents do not appear to gain much benefit from their variable modulus springs. At the intended static deflection point the spring rate is well above the low spring rate which exists at low deflection. If such a damper is operated at or near balanced load condition (drilling weight equals pump apart force), where the static deflection is zero or low, the damper will bang against its travel limit stop on alternate half cycles of vibration. Even when operating at the middle of the load-deflection curve, such a damper may bang its expansion limit stop, since as in any single acting damper there is no spring opposition to extension of the damper from its partially contracted condition; in fact, the spring assists the extension.
Some account of the foregoing problem is taken in the damper disclosed in U.S. Pat. No. 4,139,994--Alther, wherein an additional spring element is provided for reverse loading. However the reverse load spring element is operative only when the bit is off bottom or the bit is lightly loaded, and has a much shorter stroke than the direct loading spring element. As stated in the brochure of Drilco Industrial entitled "Shock Sub" with reference to a commercial embodiment of the Alther damper:
In the aforementioned copending application of William R. Garrett there is disclosed a drill string damper which is especially constructed for balanced load drilling wherein the drilling weight and pump apart force are substantially equal, the damper including resilient means that is strained equally by like axial displacements of the spring means from the neutral or unstrained position in the direction of extension and the direction of contraction of the damper. The resilient means has a low spring modulus at positions near the neutral position and a higher modulus at positions farther from the neutral position. With this construction, the damper can operate at the very low modulus range of the spring means over an expected travel range, but will convert to a high modulus damper at each end of the stroke to prevent banging against the travel stops.
As set forth in the Garrett application, it was originally conceived that such a double acting variable modulus damper might employ as the spring means a stack of annular pads of felted steel wire, or a stack of elastomer-metal washer sandwiches, or a stack of Belleville springs. All of such spring elements have various drawbacks. Wire pads have high internal friction and tend to crush and lose their resiliency when overstressed or fatigued; elastomer-metal sandwiches are subject to rapid deterioration in high temperature surroundings; ordinary Belleville springs, if designed to have a large variation in springs rate, will likely be stressed near or over the elastic limit, reducing their life expectancy.
None of the aforementioned all metal spring means has as wide a range of spring rates as is desirable. In this regard it is to be noted that an equation giving TR, the ratio between the magnitude of a transmitted vibratory force and an impressed vibratory force, is EQU TR=[(1+(2zr).sup.2 ]/[(1-r.sup.2).sup.2 +(2zr).sup.2)].sup.1/2
where r is the ratio of the impressed frequency to the natural frequency, and z is the damping factor. See eq. 2-87 on p. 72 and equation 2-41, on page 40 of the treatise entitled Mechanical Vibrations by Rolland T. Hinkle published 1963 by Allyn and Bacon, Inc. A curve plotting the relationship of TR and r, taken from FIG. 2.32 on page 73 of the aforementioned treatise, appears as FIG. 10 of the accompanying drawings. From the curve it will be seen that the least transmission of force occurs for damping means which have a ratio r larger than (2).sup.1/2 and which have the smallest possible damping factor z. Conversely, it will be seen that if the ratio r is less than (2).sup.1/2, there is a possibility of resonant vibration, unless the system is frictionally damped.
It may be assumed that in rotary drilling employing a three cone rock bit, the drill string rotating at 60 revolutions per minute, the impressed vibratory force as the bit moves past a rock or other high spot in the bottom of the hole is (3).times.(60)=180 cpm or 3 cps. It is therefore desirable that the natural frequency of the system comprising the damper and drill stem thereabove be less than 3/(2).sup.1/2 =circa 2 cps.
It is an object of the present invention to provide a damper which will be soft enough to provide a natural frequency as low as possible over a wide range of deflection, with a gradually, then rapidly, increasing spring stiffness to provide a cushioned stop at the ends of the damper stroke as defined by the travel limit stops. A further object of the invention is to provide such a damper which will have a long life even under high temperature conditions. Other objects and advantages of the invention will appear from the following description thereof.